Methods of making dry adhesives

ABSTRACT

Dry adhesives and methods of making dry adhesives including a method of making a dry adhesive including applying a liquid polymer to the second end of the stem, molding the liquid polymer on the stem in a mold, wherein the mold includes a recess having a cross-sectional area that is less than a cross-sectional area of the second end of the stem, curing the liquid polymer in the mold to form a tip at the second end of the stem, wherein the tip includes a second layer stem; corresponding to the recess in the mold, and removing the tip from the mold after the liquid polymer cures.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from U.S. provisional patentapplication No. 61/192,482, filed Sep. 18, 2008, now abandoned, andwhich is incorporated by reference herein. This application is relatedto U.S. patent application Ser. No. 12/448,242, filed Jun. 12, 2009, andU.S. patent application Ser. No. 12/448,243, filed Jun. 12, 2009. Thisapplication is related to United States patent application entitled “DryAdhesives and Methods of Making Dry Adhesives”, filed Sep. 18, 2009,under Ser. No. 12/562,643.

STATEMENT REGARDING FEDERALLY-SPONSORED RESEARCH AND DEVELOPMENT

This invention was made, in part, with government support under GrantNumber CMMI-0900408 awarded by the National Science Foundation. TheUnited States government may have certain rights in this invention.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to dry adhesives, and methods for makingdry adhesives including, for example, fibrillar microfibers andnanofibers.

Fibrillar Adhesives in Nature

Nature provides endless inspiration for solutions to engineeringchallenges. Particularly at the small (sub-millimeter) scale, millionsof years of evolution has resulted in fascinating structures withunique, sometimes non-intuitive properties. In the case of small agileclimbing animals, fibrillar foot-pads as a solution for grippingsurfaces has evolved many times. Similar structures are present inanimals of different phyla, including arthropods (spiders, insects), andchordates (lizards), suggesting independent evolution. There is alsoevidence that these structures evolved independently within differenttypes of lizards (Geckos, Anoles, and Skinks), with slightly differentresulting structures [D. Irschick, A. Herrel, and B. Vanhooydonck,“Whole-organism studies of adhesion in pad-bearing lizards: creativeevolutionary solutions to functional problems,” Journal of ComparativePhysiology A: Neuroethology, Sensory, Neural, and Behavioral Physiology,vol. 192, no. 11, pp. 1169-1177, 2006].

There exist a wide variety of fibrillar adhesives across the widevariety of animals, which utilize these structures. Some insects havefibrillar foot pads which secrete oily fluids which aid in adhesion,while others have completely dry structures. Adhesive pads which do notutilize secretions are called ‘dry adhesives,’ as they leave no residueon the surfaces to which they adhere. Dry adhesives exhibit many uniqueadhesive properties. They act similar to a pressure sensitive adhesivesuch as tape, but are highly repeatable with long lifetimes, do notrequire cleaning, and, often in combination with small claws, adhere tosurfaces which are anywhere from atomically smooth silicon to extremelytextured rock. Furthermore, they exhibit directional properties,adhering in one direction, and easily releasing from the surface whenloathed in another. Adhesion pressures as high as 200 kPa have beendemonstrated for gecko subdigital toepads and single fiber (seta)measurements exhibited adhesion pressures greater than 500 kPa (50N/cm²)[K. Autumn, “Biological Adhesives,” Springer Berlin Heidelberg, 2006].Using advanced fibrillar adhesives, several gecko species are capable ofcarrying up to 250% of their own body weight up a smooth verticalsurface. Dry fibrillar adhesives are also quite power efficient. Theycan be attached and detached from surfaces with very low forces by meansof special loading and peeling motions. Once adhered to a surface, theyrequire no power to maintain contact, and resist detachment for longperiods of time.

Interestingly, and against intuition, the material that makes lip thesehigh performance adhesive footpads is not sticky at all. The fibers aremade from a β-keratin, much like bird claws and feathers. It is thesmall size-scale and geometrical structure, which allows this materialto act as a powerful and versatile attachment mechanism.

Mechanics of Fibrillar Adhesion

The hairlike structures of gecko footpads have fascinated scientists forwell over a century, with various hypotheses about the mode ofattachment. In 1884, Simmermacher proposed the hypothesis that geckolizards might adhere to surfaces using micro-suction cups [G.Simmermacher, “Untersuchungen ber haftapparate an tarsalgliedern voninsekten,” Zeitschr. Wiss. Zool, vol. 40, pp. 481-556, 1884]. Fiftyyears later, Dellit carried out experiments in a vacuum winchdemonstrated that suction is not the dominant attachment mechanism ingeckos [W. D. Dellit, “Zur anatomie and physiologie der geckozehe,”Jena. Z. Naturw, vol. 68, pp. 613-656, 1934]. Similarly, electrostaticadhesion and micro-interlocking were ruled out. It was not until theadvent of the Scanning Electron Microscope that scientists were able toinvestigate the true structure of these microscopic features. What theyobserved is a forest of microscale fibers, each branching into finer andfiner hairs, ending in spatula-like tips. It is this structure thatturns the stiff keratin into a capable adhesive.

Conventional pressure sensitive adhesives such as adhesive tapes, gels,and soft elastomers function by deforming into the shape of thecontacting surface when pressed into contact. Materials with very lowYoung's modulus (stiffness) conform to surfaces to create large contactareas and do not store enough elastic energy to induce separation fromthe surface after the loading is removed. However, due to their lowmodulus, these materials tend to pick up contaminants from the surface,and are typically not re-usable.

Stiffer materials do not easily conform to surface roughness, and ifdeformed into intimate contact through high loading, store enoughelastic energy to return to their original shape, peeling away from thesurface in the process of relaxation. Bulk stiff materials generally donot exhibit tackiness or adhesion due to this self-peeling behavior.

The structures found in the attachment pads of the animals describedabove consist of arrays of thousands or millions of hair-like fibers,which stanch vertically or at an angle from the pad surface. Each fiberacts independently and generally has a specialized tip structure. Thehairs in these fibrillar adhesives conform to the roughness of theclimbing surface to increase the real contact area much like thedeformation of soft adhesive tape, resulting in high adhesion by surfaceforces [K. Autumn et al., “Adhesive force of a single gecko foot-hair,”Nature, vol. 405, pp. 681-685, 2000]. This adhesion, called dryadhesion, is argued to arise from molecular surface forces such as vander Waals forces [K. Autumn et al. “Evidence for van der waals adhesionin gecko setae,” Proceedings of the National Academy of Sciences USA,vol. 99, pp. 12252-12256, 2002], possibly in combination with capillaryforces [G. Huber et al., “Evidence for capillarity contributions togecko adhesion from single spatula nanomechanical measurements,”Proceedings of the National Academy of Sciences USA, vol. 102, pp.16293-16296, 2005]. Although the total potential contact area of asurface broken up into fibers is less than the area of a flat surfacebecause of the gaps between the fibers, the ability for each fiber tobend and conform to the surface roughness allows thousands, millions orbillions of fibers no make small individual contacts, which add up to alarge surface area. In comparison, a flat surface only makes contactwith the asperities of a surface, and since the deformations of bulkmaterial are typically small, the total contact area is much less thanin the fibrillar case. An illustration of this comparison can be seen inFIG. 1, which illustrates the contact area of a flat stiff material 2against a rough surface 4 (FIG. 1 a) can be less than the contact areaof a fibrillar adhesive 6 against the same surface 4 (FIG. 1 b) despitethe area lost between the fibers.

Because of the high aspect ratio (height to diameter) of the fibers inFIG. 1 b, the fibrillar surface's effective modulus is low despite thematerial modulus typically being quite high. The keratinous materialsfound in geckos' fibers are estimated to have a Young's modulus ofapproximately 1-2.5 GPa. However, due to their hairy structure, theeffective modulus is closer to 100 kPa, much like a soft tackyelastomer.

Animals with very low mass, such as insects, generally have a simplymicro-fiber structure with specialized tips. In large lizards such asthe Tokay gecko the fibers take on a complicated branched structure withmicroscale (4-5 μm) diameter base fibers which branch down to sub-micron(200 nm) diameter terminal fibers. At the end of these terminal fibersare specialized tips.

The most advanced fibrillar dry adhesives are found in the heaviestanimals such as the Tokay and New Caledonia Giant Gecko gecko which canweigh up to 300 grams. Gecko toes have been shown to adhere with highinterfacial shear strength to smooth surfaces (88−200 kPa). Theseanimals have adhesive pads with many levels of compliance includingtheir toes, foot tissue, lamellae, and fibers. This multi-levelhierarchy allows the adhesives pads to conform to surface roughness withvarious frequency and wavelength scales. The fibers are angled withrespect to the animals' toes, and the branched tips are also orientedwith respect to the base of the fiber. The result is that the gecko padexhibits a high level of directional dependence, high adhesion whiledragging the toe inwards, and no adhesion in the opposite direction.This directionality is sometimes referred to as frictional anisotropyor, more appropriately, directional adhesion.

Studies of gecko footpads have revealed that due to their asymmetricangled structure, they are non-adhesive in their resting state, and adragging motion is required to induce adhesive behavior [K. Autumn etal., “Frictional adhesion: a new angle on gecko attachment,” Journal ofExperimental Biology, vol. 209, pp. 3569-3579, 2006]. Reversing thedirection of this dragging motion removes the fibers from the surfacewith very little force.

Motivation for Fabrication of Dry Adhesives

The dry fibrillar adhesive structures found in nature exhibitproperties, which may be highly desirable in synthetic materials. Themechanics which gives rise to the adhesion in these structures does notrely on liquids or pressure differentials, therefore fibrillar dryadhesives are uniquely suited for a variety of uses. Since dry adhesivesleave no residue and can grip over large areas, they could be used asgrippers for delicate parts for transfer and assembly of anything fromcomputer chips in a clean-room to very large porous carbon-fiber panelsfor vehicle construction.

If manufactured inexpensively, synthetic dry adhesives could also finduses in daily life as a general adhesive tape for hanging items,fastening clothing, or as a grip enhancement in athletic activities suchas gloves, shoes, and grips.

Man-made dry adhesives might be used for temporary attachment ofstructures during assembly, or allow astronauts to grip the smooth outersurfaces of spacecraft during extra-vehicular missions.

Since biological dry adhesives allow animals to climb on smoothsurfaces, synthetic dry adhesives should enable robots to do the same.Robots with dry adhesive grippers may be used for inspection and repairof spacecraft hulls, or terrestrial structures. Since the adhesivesrequire no power to remain attached, climbing robots could perch fordays, weeks, or months with very little power usage. Also, due to thepower efficient attachment and detachment, robots might move as easilyup a wall as they currently traverse the ground. Similarly, one day,gloves covered in synthetic dry adhesives might allow humans to easilyscale smooth vertical surfaces.

There are potential applications for fibrillar adhesives in the field ofmedicine as well. Safe, non-destructive temporary tissue adhesives couldassist in surgical procedures. Capsule endoscopes might use fibrillaradhesives to anchor to intestine walls without damaging the tissue inorder to closely examine or biopsy an area of interest. Fibrillaradhesives may also be designed for attachment to skin as an alternativeto conventional adhesive bandages and patches.

2. Prior Art

Synthetic Fibrillar Adhesives

In 2000, when Autumn et al. published work measuring the adhesion of asingle gecko seta, suggesting that it is the van der Waalsintermolecular forces dominantly, which allow geckos to climb, itspawned a field of research into understanding and modeling theunderlying principles of fibrillar adhesion, and fabricating syntheticmimics. Soon after, Autumn et al. demonstrated van der Waals forces anda unique geometry are primarily responsible for the adhesion. Sitti andFearing created the first synthetic fibrillar adhesives by siliconerubber micromolding in the same year [M. Sitti and R. S. Fearing,“Nanomolding based fabrication of synthetic gecko foothairs,” InProceedings of the IEEE Nanotechnology Conference, pp. 137-140, 2002].

In the years since then, there has been a flurry of research, with morethan 50 publications on the topic in 2007 alone. Autumn continues totest biological specimens which provide insights into the mechanisms ofadhesion, self cleaning [W. R. Hansen and K. Autumn, “Evidence forself-cleaning in gecko setae,” Proceedings of the National Academy ofSciences USA, vol. 102, no. 2, pp. 385-389, 2005], and the directionalproperties of real gecko setae.

Huber and Sun demonstrated evidence that suggests that capillary forcesof ambient water layers on surfaces play a significant role in fibrillaradhesion. Contact mechanics researchers such as Persson, Crosby, and Huihave investigated the crack trapping nature of patterned and fibrillarsurfaces, which they have shown to increase the adhesion and toughnessof the interfaces. In addition, Hui studied the bending and bucklingnature of fibrillar surfaces, and the effects of this behavior on theadhesion of simple pillars. Arzt has investigated the effects of scaleand shape of natural fibrillar adhesives, concluding that tip shape hasless importance at smaller size scales. Several groups have demonstratedan inverse correlation between animal size and fibril tip dimension,with the heaviest animals having the finest fiber structures [E. Arzt,S. Gorb, and R. Spolenak, “From micro to nano contacts in biologicalattachment devices,” Proceedings of the National Academy of SciencesUSA, vol. 100, no. 19, pp. 10603-10606, 2003].

The mechanics of fiber to fiber interactions have been studied andmodeled to determine the proper spacing and patterning for a highdensity of fibers without clumping. Fibers will clump together if theadhesion energy between neighboring fibers is greater than the storedelastic energy of the fibers bending into contact. The resultingequations can be used to calculate the closest spacing without permanentcollapse.

The effects of crack trapping on increasing the toughness and adhesionof fibrillar surfaces have been studied on the macro-scale as well asthe micro-scale. Several structures have been tested, and showenhancement over non-fibrillated structures.

The roughness adaptation of gecko pads has also been investigatedthrough testing and modeling. The mechanics of fiber deformation andbuckling reveals that fibrillar structures can decrease the effectivemodulus of the surface by several orders of magnitude, allowingconformation to various rough and curved surfaces.

In addition to research to understand and model the mechanics ofadhesion, several research groups have developed fabrication techniquesto create synthetic fibrillar arrays. Since van der Waal's forces areuniversal, a wide variety of materials and techniques may be used toconstruct the fibers. Initially, simple vertical fiber arrays werefabricated from various materials such as polymers. Methods such aselectron-beam lithography, micro/nanomolding, nanodrawing, andself-assembly are employed to fabricate fibers from polymers, polymerorganorods, and multi-walled carbon nanotubes.

Generally, arrays of simple pillar structures were not effective inincreasing the adhesion of surfaces. Significant adhesion enhancementwas demonstrated only when the flat tips of the structures werefabricated to have higher radii for increased contact area. Gorb et al.fabricated polyvinylsiloxane fibers with thin plate flat mushroom tipswhich demonstrated adhesion enhancement as well as contaminationresistance [S. Gorb et al., “Biomimetic mushroom-shaped fibrillaradhesive microstructure,” Journal of The Royal Society Interface, vol.4, pp. 271-275, 2007]. Similarly, Del Campo et al. developed techniquesfor forming flat mushroom tips as well as more complex 3D geometries,including asymmetric tips, by dipping [A. Del Campo et al., “Patternedsurfaces with pillars with controlled and 3d tip geometry mimickingbioattachment devices,” Advanced Materials, vol. 19, pp. 1973-1977,2007]. Kim et al. developed fabrication methods to form microscalefibers with flat mushroom tips by exploiting the champagne glass effectduring Deep Reactive Ion Etching to form negative templates in siliconon oxide wafers [S. Kim and M. Sitti, “Biologically inspired polymermicrofibers with spatulate tips as repeatable fibrillar adhesives,”Applied Physics Letters, vol. 89, no. 26, pp. 261911, 2006]. Inaddition, Kim demonstrated the importance of controlling the thicknessof the backing layer in order to reduce coupling between fibers.

Glassmaker et al. fabricated polymer fibers topped with a terminal filmwhich exhibited adhesion enhancement over tipless pillars andunstructured surfaces [Nicholas J. Glassmaker et al., “Biologicallyinspired crack trapping for enhanced adhesion,” Proceedings of theNational Academy of Sciences, vol. 104, pp. 10786-10791, 2007]. Angledpillars with a terminal film have also been fabricated with directionalproperties [H. Yao et al., “Adhesion and sliding response of abiologically inspired fibrillar surface: experimental observations,”Journal of The Royal Society Interface, vol. 5 no. 24, pp. 723-7332007]. By angling the pillars beneath the terminal film, the resultantstructure exhibits anisotropic adhesion. In addition to stem angle, theangle of the surface of the tip with respect to the stem is as crucialin terms of controlling the anisotropic behavior in adhesion andfriction. Kim et al. [S. Kim et al., “Smooth Vertical Surface ClimbingWith Directional Adhesion,” IEEE Transactions on Robotics, vol. 24, no.1, pp. 1-10, 2008] fabricated synthetic sub-millimeter wedges with thestem and tip surface of each individual wedge oriented at an angle withrespect to the backing layer of the wedge array. These structuresexhibited anisotropic friction much-like the biological counterparts.While the magnitude of friction was an order of magnitude less than thebiological gecko footpads, adhesion in normal direction was negligible.Later Asbeck et al. [A. Asbeck et al., “Climbing rough vertical surfaceswith hierarchical directional adhesion,” IEEE International Conferenceon Robotics and Automation, Kobe, Japan, 2009] fabricated similarlyshaped wedges that are an order of magnitude smaller which showedsimilar adhesion performance to the sub-millimeter wedges. Adhesionimprovement, still low compared to the biological gecko footpad,occurred when they topped sub-millimeter wedges with a terminal filmcomprised of micro-wedges.

Higher modulus synthetic fibrillar adhesives have been developed on thesub-micron diameter scale. These fibers, made from stiffer materials(E≧1 GPa) such as polypropylene, polyimide, and nickel, carbonnanofibers and carbon nanotubes. Although these stiffer fibers do notadhere well in the normal direction, and require high preloads to makeintimate contact, shear adhesion pressures of up to 36 N/cm², which ishigher than the adhesion strength of the gecko, have been demonstrated.

To more closely mimic the structure of the gecko's foot hairs, work hasalso been done to fabricate hierarchical fibers with multi-levelstructures. Ge et al. bundled carbon nanotubes into pillars which deformtogether but have individually exposed tips. [L. Ge et al., “Carbonnanotube-based synthetic gecko tapes,” Proceedings of the NationalAcademy of Sciences, vol. 104, no. 26, pp. 10792-10795, 2007].Photolithography has been used to fabricate simple micro-pillars on topof base pillars [A. Del Campo and E. Arzt, “Design parameters andcurrent fabrication approaches for developing bioinspired dryadhesives,” Macromolecular Bioscience, vol. 7, no. 2, pp. 118-127,2007]. On the millimeter scale, Shape Deposition Manufacturing has beenused to fabricate hierarchical structures in thin polymer plates, whichare stacked into arrays [M. Lanzetta and M. R. Cutkosky, “Shapedeposition manufacturing of biologically inspired hierarchicalmicrostructures,” CIRP Annals—Manufacturing Technology, vol. 57, pp.231-234, 2008]. Kustandi et al. demonstrated a fabrication technique touse nanomolding in combination with micromolding to create ahierarchical structure with superhydrophobic properties.

In addition to dry adhesives, other work is being conducted on syntheticfibers with oily coatings, inspired by beetle adhesion, which exhibitincreased adhesion over uncoated structures.

The microfiber fabrication methods described above are very expensivefor producing commercial quantities of adhesive materials. Moreover,they cannot efficiently and controllably produce angled fibers withspecialized tips or hierarchical structures with specialized tips.Accordingly, there is a need for improved dry adhesives and improvedmethods for making dry adhesives. In particular, there is a need for dryadhesives having greater adhesive forces and improved durability. Inaddition, there is a need for methods of making dry adhesives with lowercosts of production. Those and other advantages of the present inventionwill be described in more detail hereinbelow.

BRIEF SUMMARY OF THE INVENTION

The present invention includes adhesives, methods for making adhesives,and fibers made according to those methods. Many embodiments arepossible with the present invention. For example, the present inventionprovides methods to fabricate fibrillar structure which have specializedtips that increase adhesion, and provide directionality to adhesion.Methods are described to fabricate fibrillar structures with angledtips. Methods are also provided to fabricate hierarchical fibrillarstructures.

The present invention provides methods for fabrication of vertical andangled micro- and nanofibers with adhesive qualities. The presentinvention further provides methods for the fabrication of micro- andnanofibers that have specialized tips or are hierarchically structuredwith specialized tips. Polymer micro- and nanofiber arrays arefabricated through a micro molding process which duplicateslithographically formed master template structures with a desired fibermaterial. This technique enables fabrication of fiber arraysinexpensively and with high yields, and enables the fabrication offibers with controlled angles. In the present invention, the fiber endsare then dipped in a polymer solution, prior to further processing whichcreate specialized and hierarchical tips to the fibers.

In one embodiment, after the dipping in a polymer solution, the assemblyis then pressed against a surface at a pre-determined angle to fabricateflattened tips at the ends of the fibers.

In another embodiment, fibers are fabricated using the methods of thepresent invention in different sizes, for example microfibers andnanofibers, and the smaller fibers are attached to the tips of thelarger fibers by making contact with the liquid polymer at the end ofthe larger fibers to create hierarchical structures.

In another embodiment, fibers are fabricated according to the methodsherein, dipped in a polymer solution, which is in turn molded to formhierarchical structures with smaller fiber structures attached to thetips of the larger fibers.

In another embodiment, the methods described herein are used tofabricate three-level hierarchical fiber structures.

In another embodiment, fibers are fabricated using the methods of thepresent invention, the fibers are then dipped in a polymer solution, andthe assembly is pressed against an array of smaller fibers, such ascarbon nanotubes, to form hierarchical structures.

There are several unique aspects to the fiber design described in thisapplication. One is an enlarged and oriented terminal end or tip of thefiber. The enlarged tip increases the contact area of the fiber thusenhancing the interfacial resistance to separation between the fiber andthe adhering surface. This shape also allows for more uniformdistribution of the applied stress over the fiber tip surface [A. V.Spuskanyuk et al., “The effect of shape on the adhesion of fibrillarsurfaces,” Acta Biomaterialia, vol. 4, no. 6, pp. 1669-1676, 2008].Another design aspect is the incorporation of sharp edges at theperimeter of the tip. The detachment of a single fiber usually startsfrom the edge as an edge crack followed by the propagation of this edgecrack along the entire interface, which results in complete separation.The crack starts at the edge due to the fact that the edge acts as astress concentrator and creates a singular stress state. For instance,when a soft fiber is in contact with a relatively rigid smooth surface,the stress at the edge of the fiber (σ_(e)) is singular and has theform:σ_(e)=Aσc^(−α)  (1)

In equation (1), σ is the applied stress far from contact, A is aconstant determined by the shape of the fiber, c is the distance fromthe edge of the fiber, and α is the order of stress singularitydetermined by the angle at the edge of contact [D. B. Bogy, “Twoedge-bonded elastic wedges of different materials and wedge angles undersurface traction,” Journal of Applied Mechanics, vol. 38, pp. 377-386,1971]. Note that at the edge of contact, c=0, stress is infinite.According to (1), it is possible to reduce the severity of stresssingularity and as such improve detachment resistance by reducing A andα. Enlarged tip shape featured in our fiber design allows for lower Avalues and reduces the severity of stress at the edge. In addition,sharper edges at the perimeter of the tip lower the order of stresssingularity a adding another dimension of stress reduction at thecontact edge. According to the work by Bogy, it is also possible toeliminate the stress singularity via sharper contact edges. While theoriented fashion of the stem and the base provides us with thedirectional properties, enlarged tip with sharper edges improveperformance in both gripping and releasing direction. Furthermore, weobtain high adhesion in normal direction, which is not achievable withwedge designs [S. Kim et al., “Smooth Vertical Surface Climbing WithDirectional Adhesion,” IEEE Transactions on Robotics, vol. 24, no. 1,pp. 1-10, 2008; A. Asbeck et al., “Climbing rough vertical surfaces withhierarchical directional adhesion,” IEEE International Conference onRobotics and Automation, Kobe, Japan, 2009].

Many other variations are possible with the present invention. Forexample, different materials may be used to make the fibers and the dryadhesive, and the geometry and structure of the fibers and the dryadhesive may vary. In addition, different types of etching and othermaterial removal processes, as well as different deposition and otherfabrication processes may also be used. These and other teachings,variations, and advantages of the present invention will become apparentfrom the following detailed description of the invention.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

Embodiments of the present invention will now be described, by way ofexample only, with reference to the accompanying drawings for thepurpose of illustrating the embodiments and not for purposes of limitingthe invention, wherein:

FIGS. 1 a and 1 b illustrate the contact area of a flat material and afibrillar material against a rough surface;

FIG. 2 illustrates one embodiment of a dry adhesive according to thepresent invention;

FIG. 3 illustrates the fabrication process for angled fibers withspecialized tips fabricated according to the present invention;

FIG. 4 provides SEM images of angled fibers with specialized tipsfabricated according to the present invention;

FIGS. 5-7 illustrate methods of making dry adhesives according to thepresent invention;

FIG. 8 provides data on gripping and releasing properties of materialsformed according to the present invention;

FIG. 9 illustrates fiber tip behavior under various loading conditions;

FIG. 10 provides data and associated SEM images for various fiber andtip geometries fabricated according to the present invention;

FIG. 11 provides data on the relationship between fiber tip area andlateral force;

FIG. 12 provides data and microphotographs indicating the sheardisplacement of materials fabricated according to the present invention;

FIG. 13 provides photographs illustrating the directionality of theshear force capacity of materials fabricated according to the presentinvention;

FIG. 14 illustrates the interaction between hierarchical fibrillarstructures and a rough surface;

FIG. 15 illustrates the fabrication process for embedding carbonnanotubes or nanofibers into the tips of base fibers according to thepresent invention;

FIG. 16 provides SEM images of carbon nanofibers embedded into the tipsof base fibers fabricated according to the present invention;

FIG. 17 illustrates the fabrication process for molding hierarchicalfibrillar structures according to the present invention;

FIG. 18 provides SEM images of molded hierarchical fibrillar structuresfabricated according to the present invention;

FIGS. 19-22 illustrate methods of making dry adhesives according to thepresent invention;

FIG. 23 illustrates the fabrication process for molding macro-microhierarchical structures according to the present invention;

FIG. 24 provides SEM images of molded macro-micro hierarchicalstructures according to the present invention;

FIG. 25 illustrates the fabrication process for making three-levelhierarchical fibers according to the present invention;

FIG. 26 provides SEM images of three-level hierarchical fibers accordingto the present invention;

FIG. 27 provides SEM images of two embodiments of double levelhierarchical fibers fabricated according to the present invention;

FIG. 28 provides comparison data on adhesion of unstructured, singlelevel, double level angled, and double level vertical fibrillarmaterials;

FIG. 29 provides comparison data on force-distance of unstructured,single level, double level angled, and double level vertical fibrillarmaterials;

FIG. 30 provides comparison data on force-distance of unstructured,single level, and double level vertical fibrillar materials;

FIGS. 31-31 e provide data and microphotographs of force vs. time datafor double level vertical fibrillar materials fabricated according tothe present invention; and

FIG. 32 illustrates data indicative of the repeatability of the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION

1 Introduction

Gecko toes have been shown to adhere with high interfacial shearstrength to smooth surfaces (88−200 kPa), using microscale angled fiberstructures on their feet. However, even with such large adhesionpressures, the detachment forces measured during climbing are nearlynon-existent. The gecko is able to release its adhesive toes withoutovercoming the large adhesion forces, which it relies on to climb andcling to surfaces. These animals are able to control the amount ofadhesion of its footpads during climbing by controlled motions duringdetachment.

Autumn et al. demonstrated that natural gecko setae exhibit extremefrictional anisotropy, with significant adhesive friction when draggedalong their natural curvature (‘gripping’ or ‘with’ direction), and onlyCoulomb friction in the ‘releasing’ or ‘against’ direction. When loadedin the ‘releasing’ direction, the adhesive pads are easily peeled fromthe surface. We fabricated angled fibers with un-oriented mushroom tipsto mimic this directional behavior, but no significant anisotropy wasobserved. Yao et al. observed directional adhesion and shear interfacestrength in angled sub-millimeter diameter PDMS stalks with a terminalfilm. Kim et al. have demonstrated sub-millimeter diameter angledpolymer stalk arrays with angled ends, for use in a climbing robot,which exhibit desirable anisotropic shear forces. However, both of theselarger-scale structures demonstrate significantly lower interfacialshear and adhesion strength than the gecko or microscale polymer fiberswith mushroom tips.

Fibrillar structures have also been fabricated to increase (or decrease)friction. In addition, fiber surfaces have been created which provideshear adhesion using vertical arrays of single and multi-walled carbonnanotubes. Unfortunately, these fibrillar structures require very highpreloads in order to provide interfacial shear strength. Stiffpolypropylene sub-micron diameter fibers have been shown to exhibitshear adhesion without requiring high preloading. Polyurethanemicro-fibrillar structures have demonstrated interfacial shear strengthof over 400 kPa, but due to these high forces, irreversible damageoccurs during detachment.

In this invention, we describe fabrication methods and structures thatcombine the high interfacial strength of mushroom tipped micron-scalefibers with the directionality of fiber structures with both angledstalks and tip endings. In Section 1.2, the fabrication techniques aredetailed for single level structures. Experimental results are presentedin Section 1.3, including investigation of adhesion anisotropy andadhesion control. In Section 1.4.2, the fabrication techniques formulti-level structures are detailed. Experimental results for themulti-level structures are provided in Section 1.4.6.

1.1 The Structure.

The present invention includes a variety of structures for dryadhesives. FIG. 2 illustrates one embodiment of a dry adhesive 10according to the present invention. In that embodiment, the dry adhesivestructure 10 includes a backing layer 20, a plurality of stems 22, and atip 28. The term “fiber” will sometimes be used to refer to the stem 22and tip 28 together. The term “fiber” will also sometimes be used torefer to the stem 22.

The stems 22 are attached to the backing layer 20. The illustratedembodiment shows a dry adhesive 10 having six stems 22, although a dryadhesive according to the present invention may have more or fewer thansix stems 22. It is possible that a dry adhesive 10 could have a singlestem 22 although in most applications the dry adhesive 10 will likelyhave many stems 22.

The stems 22 have first 24 and second 26 ends on opposite sides of thestem 22. The first end 24 of the stem 22 is connected to the backinglayer 20, and the second end 26 of the stem 22 is connected to the tip28.

The tip 28 includes an expanded surface 30 which is generally away fromthe stem. The expanded surface 30 is larger than the stem 22. In otherwords, the expanded surface 30 has an area that is greater than a crosssectional area of the second end 26 of the stem 22, when thecross-sectional area of the second end of the stem 22 is measured in aplane parallel to the expanded surface 30. The expanded surface 30 maybe planar or it may be non-planar. For example, the expanded surface 30may be concave or convex or it may have other features such as recessesand projections. If the expanded area 30 is non-planar, thecross-sectional area of the stem 22 can be measured parallel to a planethat most closely approximates the expanded surface 30.

In the illustrated embodiment the expanded surface 30 is not parallel tothe backing layer 20. This orientation has been found to providesuperior results with dry adhesives 10, although it is not required thatthe expanded surface 30 be non-parallel to the backing layer 20. Forexample, the present invention may also include tips 28 with an expandedsurface 30 that is parallel to the backing layer 20.

The relationship between the backing layer 20, stem 22, and tip 28 canvary in different embodiments of the present invention. In theillustrated embodiment, the stem forms an angle θ relative to a lineperpendicular to the backing layer 20. Similarly, the expanded surface30 forms an angle β−θ relative to a plane parallel to the backing layer20. The angle β can be defined during the fabrications process, as willbe described in more detail hereinbelow.

Typically, the angles θ and β are between zero and ninety degrees.However, it is possible for those angles to be greater than ninetydegrees. For example, if the backing layer 20 is non-planar, if itcontains recesses into which the stem 22 can be bent, or if it otherwisemakes allowances for the stem 20 to adopt such an orientation, then theangle θ may be greater than ninety degrees. Other variations are alsopossible, such as a J-shaped stem 22, which allows θ to be greater thanninety degrees. Similarly, it is also possible for β to be greater thanninety degrees, such as if the stem 22 takes a different shape ororientation from that illustrated herein. For example, a J-shaped stem22 may allow for the expanded surface 30 to be rotated more than ninetydegrees.

1.2 Fabrication of Specialized Tips on Single Level Structures

The fabrication process for creating directional adhesives withspecialized tips 28 begins with the fabrication of an array ofcylindrical base fibers. Angled or vertical base fiber arrays arefabricated through a micromolding process which duplicateslithographically formed master template structures with a desired fibermaterial. This method for fabrication of the fiber arrays is describedin U.S. patent application Ser. No. 12/448,242, by the same inventors,which is incorporated herein by reference.

FIGS. 3 a-3 d illustrates one embodiment of a fabrication processaccording to the present invention. In that embodiment, the fabricationprocess is used for adding angled mushroom tips 28 to fibers 22. In FIG.3 a, bare fibers 22 with angle θ are aligned with a layer of liquidpolymer 40. The liquid polymer 40 may be carried on a substrate or someother surface 44 for holding the liquid polymer 40. In FIG. 3 b, thefibers are dipped into the liquid 40 and retracted, retaining somepolymer 40 at the tips 28. In FIG. 3 c, the fibers 28 are brought intocontact with a tip-shaping surface 42, such as a substrate, and pressedwith a constant load during curing, bending the fibers 22 to angle β. InFIG. 3 d, the sample is peeled from the substrate 42 and the fibers 22return to their original angle θ, resulting in tip angle (β−θ).

In one embodiment of the present invention, 1 in² fiber arrays aremolded from polyurethane with a ≈1 mm thick backing layer using a thinspacer to define the thickness and ensure uniformity. A thin film ofliquid ST-1060 polyurethane is spun onto a polystyrene substrate for 45seconds at 4,000 rpm. The fiber array is placed on the film of liquidpolyurethane (FIG. 3 a). The liquid polyurethane wets the tips of thefibers, and then the fiber arrays are separated from the liquid film(FIG. 3 b). Next, the fiber arrays are placed onto a low surface energysubstrate and a weight, preferably (50-200 g) is placed onto the backinglayer, which bends the base fibers to desired angle β (FIG. 3 c) andforms a specialized expanded tip with desired orientation to the fibers.A variety of orientations of the tip to the fiber can be fabricated byadjusting the angle at which the fiber arrays are pressed onto thesubstrate to achieve desired adhesion and release characteristics.

The construct of the fiber array with the specialized tip material arethen cured by methods known to those skilled in the art.

The fiber arrays are then peeled from the substrate, and the fibersreturn to their initial angle (θ), tilting the tips to an angle of (β−θ)as shown in FIG. 3 d.

In one embodiment of the present invention, the microfibers havediameters of ˜35 μm and lengths of ˜100 μm, with base fiber angles from0° to 33° from horizontal. The fibers are arranged in a square gridpattern with a center-to-center spacing of 120 μm. The fiber arrays arefabricated from a polyurethane elastomer with a Young's modulus of ˜3MPa, chosen for its high tear strength and high strain before failure.

This process has been implemented to form the first synthetic fiberswith angled spatular tips. By varying the fiber geometry or the loadduring curing, the tip angle can be fabricated anywhere from 0 (no tipangle) to 90° (tips parallel to the fiber stem, see FIG. 4 b below).

FIGS. 4 a-4 d are scanning electron microscope images of arrays of 35 μmdiameter angled polyurethane microfibers with angled mushroom tips whichwere constructed according to one embodiment of the present invention.Tip orientation can be controlled to form tips with varying angles: (a)34°; (b) 90°; (c,d) 23°. Details of the tip can be seen in (d).

FIG. 5 illustrates one embodiment of a method of fabricating dryadhesive structures according to the present invention. The process mayinclude forming a dry adhesive 10 with a structure including a backinglayer 20 and stem 22 as described above. The stem 22 may be eitherperpendicular to the backing layer 20 or non-perpendicular to thebacking layer 20. As described above, the stem includes first 24 andsecond 26 ends on opposite sides of the stem 22, and wherein the firstend 24 of the stem 22 is connected to the backing layer 20 and thesecond end 26 of the stem 22 is connected to the tip 28.

Step 100 includes applying a liquid polymer 40 to the second end 26 ofthe stem 22 as described above, for example, with reference to FIG. 3 b.Although the present invention will generally be described in terms ofusing a liquid polymer 40, it is possible that other materials may alsobe used in place of liquid polymer 40.

Step 102 includes contacting the liquid polymer on the stem with a tipshaping surface. See, for example, FIG. 3 c above.

Step 104 includes bending the stem relative to the backing layer whilecontacting the liquid polymer on the stem with the tip shaping surface.See, for example, FIG. 3 c above.

Step 106 includes curing the liquid polymer to form a tip on the secondend of the stem while bending the stem relative to the backing layer andwhile contacting the liquid polymer on the stem with the tip shapingsurface. See, for example, FIG. 3 c above.

Step 108 includes removing the tip from the tip shaping surface afterthe liquid polymer cures. See, for example, FIG. 3 d above.

Many variations and modifications are possible with this method. Some ofthose variations and modifications will be described below.

For example, step 100 may include dipping the second end 26 of the stem22 in a liquid polymer 40 followed by removing the second end 26 of thestem 22 from the liquid polymer 40 after the liquid polymer 40 isapplied to the second end 26 of the stem 22. In other embodiments, theliquid polymer 40 may be applied by methods other than dipping, such asby spraying or otherwise applying the liquid polymer 40. In such cases,the step of removing the second end 26 from the liquid polymer 40 maynot be needed in some embodiments.

Step 102, contacting the liquid polymer 40 on the stem 22 with a tipshaping surface 42, may includes forming the expanded surface 30 in theliquid polymer 40 as described above. This may also include forming aplanar surface in the liquid polymer 40 where the liquid polymer 40contacts the tip shaping surface 42. The planar surface may be formed,for example, by using a tip forming surface 42 that is planar. However,other tip forming surfaces 42 may be used to form other expandedsurfaces 30 on the tip 28. For example, concave or convex tip formingsurfaces 42 may be used, as well as tip forming surfaces 42 havingrecesses, bumps, or other features that can be used to shape theexpanded surface 30 of the tip 28.

As described above, the expanded surface 30 of the tip 28 may have anarea that is greater than a cross-sectional area of the second end 26 ofthe stem 22 in a plane parallel to the expanded surface 30 of the tip28.

Step 104, bending the stem, may include applying a load to the backinglayer. This is one way of being the stem 22, although other ways mayalso be used with the present invention.

Step 104, bending the stem, may also include bending the stem 22 in adirection away from a perpendicular orientation with the backing layer20. In other words, a non-parallel stem 22 may be bent in such a way asto exaggerate or increase the extent to which the stem 22 isnon-parallel with the backing layer 20.

Step 104, bending the stem 22 relative to the backing layer 20 whilecontacting the liquid polymer 40 with the tip shaping surface 42, mayinclude bending the stem to form an angle β relative to an imaginaryline perpendicular to the backing layer, wherein β is greater than θ andless than ninety degrees, as described above.

Step 106, curing the liquid polymer cures to form a tip 28, may includeforming an expanded surface 30 in the tip 28 where the tip 28 contactsthe tip shaping surface 42, and wherein after removing the tip 28 fromthe tip shaping surface 42 the expanded surface 30 of the tip 28 formsan angle β−θ relative to an imaginary plane parallel to the backinglayer 20.

Step 106, curing the liquid polymer 40 to form a tip 28, may includeforming the expanded surface 30 on the tip 28 where the tip 28 contactsthe tip shaping surface 42. In other words, the shape of the expandedsurface 30 may be formed during the curing step 106, when the liquidpolymer 40 on the stem 22 changes from liquid form to cured or solidform and retains the general shape at the time of curing. As a result,curing the liquid polymer 40 forms an expanded surface 30 indicative ofthe tip shaping surface 42.

After step 108, removing the tip 28 from the tip shaping surface 42, theexpanded surface 30 of the tip 28 may be planar and not parallel to thebacking layer 20, as described in more detail herein.

After step 108, removing the tip from the tip shaping surface, themethod of the present invention may result in a stem 22 that forms anangle θ relative to an imaginary line perpendicular to the backing layer20, wherein θ is greater than zero degrees and less than ninety degrees.As described above, it is also possible for θ to be greater than ninetydegrees. Other values for θ are also possible with the presentinvention. For example, θ may be zero degrees if the stems 22 areperpendicular to the backing layer 20.

Many other variations and modifications are also possible. For example,the method may also include maintaining the backing layer 20 parallel tothe tip shaping surface 42 during step 104, when bending the stem 22relative to the backing layer 104. The method may also includemaintaining the backing layer 20 parallel to the tip shaping surface 30during step 106, curing the liquid polymer 106. In other embodiments,the backing layer 20 may be maintained non-parallel to the tip shapingsurface 42.

FIG. 6 illustrates another embodiment of the method according to thepresent invention. That method includes forming a dry adhesive 10 with astructure including a backing layer 20 and a non-perpendicular stem 22,wherein the stem 22 includes first 24 and second 26 ends on oppositesides of the stem 22, and wherein the first end 24 of the stem 22 isconnected to the backing layer 20.

Step 200 includes applying a liquid polymer 40 to the second end 26 ofthe stem 28.

Step 202 includes contacting the liquid polymer 40 on the stem 22 with atip shaping surface 42.

Step 204 includes forming an expanded, planar surface in the liquidpolymer 40 where the liquid polymer contacts the tip shaping surface 42.

Step 206 includes bending the stem 22 relative to the backing layer 20while contacting the liquid polymer 40 on the stem 22 with the tipshaping surface 42, wherein bending the stem 22 includes bending thestem 22 in a direction away from a perpendicular orientation with thebacking layer 20.

Step 208 includes maintaining the backing layer 20 parallel to the tipshaping surface 42 when bending the stem 22 relative to the backinglayer 22.

Step 210 includes curing the liquid polymer 40 to form a tip 28 on thesecond end 26 of the stem 22 while bending the stem 22 relative to thebacking layer 20 and while contacting the liquid polymer 40 on the stem22 with the tip shaping surface 42, wherein the expanded surface of theliquid polymer forms an expanded surface 30 of the tip 28 during curing,wherein the expanded surface 30 of the tip 28 has an area that isgreater than a cross-sectional area of the second end 26 of the stem 22in a plane parallel to the expanded surface 30 of the tip 28.

Step 212 includes maintaining the backing layer 20 parallel to the tipshaping surface 42 when curing the liquid polymer 40.

Step 214 includes removing the tip 28 from the tip shaping surface 42after the liquid polymer 40 cures, wherein the expanded surface 30 ofthe tip 28 is not parallel to the backing layer 20 after removing thetip 28 from the tip shaping surface 42.

Many variations and modifications are possible according to the presentinvention. For example, after removing the tip 28 from the tip shapingsurface 42, the method of the present invention may result in a stem 22that forms an angle θ relative to an imaginary line perpendicular to thebacking layer, wherein θ is greater than zero degrees and less thanninety degrees. Other values for θ are also possible with the presentinvention.

Step 206, bending the stem 22 relative to the backing layer 20 whilecontacting the liquid polymer 40 with the tip shaping surface 42, mayinclude bending the stem 22 to form an angle β relative to an imaginaryline perpendicular to the backing layer 20, wherein β is greater than θand less than ninety degrees. Other values for θ and β are also possiblewith the present invention.

Step 210, curing the liquid polymer 40 form a tip, may include formingan expanded surface 30 in the tip 28 where the tip 28 contacts the tipshaping surface 42. Also, after step 214, removing the tip 28 from thetip shaping surface 42, the expanded surface 30 of the tip 28 may forman angle (β−θ) relative to an imaginary plane parallel to the backinglayer 20.

Other variations and modifications are also possible with the presentinvention.

1.3 Friction Anisotropy: Results

Shear and normal adhesion of our angled fiber arrays with specializedtips fabricated with the methods of the present invention as describedabove were measured in a variety of ways to investigate interfacialshear strength, directionality, and the controllability of adhesion. Inone measurement method, normal and shear forces were measured during afixed shear displacement of 500 μm between a 6 mm diameter glassspherical indenter and the fiber array. In a second set of experimentswith the same indenter, we measured the effect of varying sheardisplacements on the resulting shear and normal forces.

A custom adhesion characterization system, described previously [B.Aksak, M. P. Murphy, and M. Sitti, “Adhesion of biologically inspiredvertical and angled polymer microfiber arrays,” Langmuir, vol. 23, no.6, pp. 3322-3332, 2007], was used for the adhesion and shearexperiments. FIG. 8 illustrates those experiments. FIG. 8 a is anillustration of the displacements in the experiments. An initialvertical preload (1) is followed by a shear displacement (2) in eitherthe ‘gripping’ direction or the ‘releasing’ direction. FIGS. 8 b and 8 cillustrate shear and normal forces during shear displacements after a 5mN preload. Positive normal force values indicate compression, andnegative values indicate adhesion. Positive shear displacementsrepresent motion in the ‘gripping’ direction, and negative sheardisplacements represent displacement in the ‘releasing’ direction.Fibers with no tip angle (FIG. 8 b) show nearly isotropic shearbehavior. For samples with 28° angled tips (FIG. 8 c) the shear forcesduring displacements in the ‘gripping’ direction are significantlyhigher than those seen in the ‘releasing’ direction, and are accompaniedby adhesive force in the normal direction.

The experiments will now be described in more detail. In the fixeddisplacement experiments, an indenter was pressed into contact with thefibers to a specified preload value of 5 mN (FIG. 8 a). When the preloadis complete, approximately 30 fibers were in contact with the indenter.Next a shear displacement between the fibers and sphere was applied at aspeed of 25 μm/s for 500 μm in either the ‘gripping’ direction or in theopposite ‘releasing’ direction while the vertical indentation depth washeld constant. Data from these experiments for fibers with no tip angle,and tip angle samples are shown in FIGS. 8 b, c, respectively. All datain each plot were taken at the same spot, and the close spacing of thedata illustrate the repeatability of the adhesion.

The fibers with no tip angle (FIG. 8 b) exhibit similar magnitudes ofthe shear forces in both directions, although the behaviors are notidentical due to the non-vertical angle of the base fiber. Fiber arrayswith no tip angle were found to have shear force anisotropy ratios (theratio of the maximum shear force in the ‘gripping’ direction to themaximum shear force in the ‘releasing’ direction) as low as 1.07:1.During these trials, the fiber tips were observed to adhere to theindenter and stretch when sheared in either direction, resulting insimilar adhesive characteristics.

In contrast, the results from the angled tip fiber sample (FIG. 8 c)indicate highly anisotropic behavior. The mean maximum shear force inthe ‘gripping’ direction is 5.6 times greater than the one observed inthe ‘releasing’ direction (a 5.6:1 shear force anisotropy ratio). Also,the compressive normal force in the releasing direction tests indicatesthat the shear forces observed were due to classical Coulomb friction.In the ‘gripping’ direction experiments, the normal force is adhesive,meaning that the mode of shear force generation cannot be Coulombfriction, which requires a compressive normal force. Rather, it is theshear component of the attached fibers under tension. Furthermore,visual observations of these tests reveal that the fiber tips adhere andstretch when displaced in the ‘gripping’ direction, whereas the tipsflip over and slide when displaced in the ‘releasing’ direction. Thissliding behavior suggests that the fibers quickly detach and cannotsupport normal loading. In other words, they may be easily separatedafter being displaced in this direction.

The measured anisotropic characteristics of the angled tip samples fromFIG. 8 c are quite similar to the characteristics of real gecko setae asmeasured by Autumn et al. The gecko setae exhibit a similar shear forceanisotropy ratio of ˜4.5:1, and similar normal force characteristics.

Although the asymmetric geometry of fiber tips can result in asymmetricstress distributions at the edges of the contact interface as describedby Bogy, we hypothesize that the observed anisotropic behavior arisesprimarily due to the stresses caused by the moment created when the tipis sheared. This can be understood by qualitative analysis of therotation of the tip during shear loading in each direction (FIG. 9).

FIG. 9 illustrates tip behavior under various loading conditions. Tipangle θ is illustrated beneath each side view illustration with respectto φ₀. FIG. 9 a illustrates original unloaded geometry. FIG. 9 billustrates a fiber under preload compression. FIG. 9 c illustratesshearing the fiber in the ‘releasing’ direction creates large tiprotation, FIG. 9 d illustrates shearing the fiber in the ‘gripping’direction reduces the tip rotation, returning to the original φ₀ beforeincreasing the tip 28 rotation in the opposite direction.

Any rotation angle of the tip 28 with respect to its originalorientation causes a peeling moment, which, in combination with shearand tensile stresses at the interface, can cause an edge of the tip 28to detach. When a fiber is compressed into intimate contact with asurface, the tip angle rotates from its original angle φ₀ (FIG. 9 a) toa larger angle φ_(c) (FIG. 9 b). The change in angle, Δφ, introduces amoment which is relative to the magnitude of the angle change from itsundeformed state. The peeling moment is increased if the fiber issheared in the releasing direction because it increases the alreadypresent tip 28 rotation to a larger angle (φ_(r)), increasing Δφ as seenin FIG. 9 c. This increased moment peels the leading edge (A),eventually detaching and overturning the fiber tip 28, as seen inprevious studies of mushroom shaped fibers. However, when sheared in the‘gripping’ direction the fiber tip 28 begins to return to its originalangle, reducing the moment to zero (FIG. 9 d). When the magnitude of themoment is near zero, the normal stress distribution at the interface ismore evenly distributed, reducing the chances of detachment. After thispoint, if the shearing in the ‘gripping’ direction is continued, Δφchanges sign and begins to increase in magnitude, eventually causing theleading edge (B) to detach. The initial decrease in moment for shearingin the ‘gripping’ direction increases the allowable displacement beforedetachment occurs, in contrast to the ‘releasing’ direction where themoment increases immediately. The increased displacement in the‘gripping’ direction allows the fibers to stretch and maintain contact,leading to high interfacial shear strength and anisotropy.

Three samples with varying geometry were tested using the sameexperimental setup outlined above. The resulting data from threerepresentative samples are plotted together along with SEM images of thesamples in FIG. 10. In particular, FIG. 10 illustrates anisotropy testdata for three samples in which columns from left to right illustrate:normal and shear forces in the ‘releasing’ direction and grippingdirection, SEM images of samples in profile view. Fibers with higher tipangle exhibit higher anisotropy.

Maximum shear force was not found to have any direct dependence on basefiber angle) (51-78°), tip angle (0-34°), base fiber diameter (32-45μm), or base fiber length (74-105 μm) within the variations between thesamples. However, a strong correlation was seen between maximum shearforce and tip area, as illustrated in FIG. 11.

FIG. 11 illustrates maximum measured lateral force has direct dependenceon tip area. This relationship confirms that mushroom tips with largecontact areas are beneficial for creating high shear adhesion, similarto the dependence of normal adhesion on tip area investigatedpreviously. Also, the degree of anisotropy was seen to be correlatedwith tip angle, where larger tip angles resulted in larger differencesbetween the shear resistances in the ‘releasing’ and ‘gripping’directions, which is consistent with the expectations from the aboveanalysis. These results indicate that tip area can be used as a designparameter to control the level of adhesion, while tip angle can be usedto design for desired levels of anisotropy.

1.3.1 Adhesion Control

It has been shown that a shear displacement is required beforebiological gecko foot-hairs (setae) can provide adhesion to a surface.To demonstrate the ability to control adhesion of our microfiber arraysvia shear displacement, a separate set of experiments was performed.

FIG. 12 illustrates how adhesion is controllable by varying the sheardisplacement of the fibers during loading. In summary, FIG. 12 a is anillustration of the displacements in the Load-Drag-Pull experiments.FIG. 12 b illustrates experimental data of maximum adhesion valuesduring normal direction separation following varying sheardisplacements, as well as maximum shear forces during sheardisplacement. FIGS. 12 c-12 e illustrate maximum vertical stretching offibers before detachment, following varying shear displacements of: (c)100 μm (releasing direction); (d) 50 μm (gripping direction), (e) 75 μm(gripping direction), (Scale bar: 100 μm).

FIG. 12 will now be described in more detail. FIG. 12 a illustrates thedisplacements of the indenter in the ‘adhesion control’ experiments.First the indenter was moved into contact with the fibers to apply a 5mN preload force (step 1). Next, a variable shear displacement wasapplied between the surfaces in either the ‘gripping’ or ‘releasing’direction. Finally, the indenter was retracted away from the fibers.This type of experiment is sometimes referred to as Load-Drag-Pull (LDP)[K. Autumn et al., “Frictional adhesion: a new angle on geckoattachment,” Journal of Experimental Biology, vol. 209, pp. 3569-3579,2006]. The maximum shear force during the shear displacement phase (step2) and the maximum adhesion measured during the shear displacement orretraction phase, whichever is higher, (step 3) are plotted for varyingshear displacements in FIG. 12 b.

The results in FIG. 12 b confirm that, similar to gecko setae, adhesioncan be controlled by lateral displacement during initial contact.Experiments with zero shear displacement, or displacement in the‘releasing’ direction of any magnitude, result in negligible adhesionand low shear forces. This is the same behavior observed by Autumn etal. in the natural gecko setae. However, displacements in the ‘gripping’direction resulted in large detachment forces in the normal direction,and generated significantly higher shear forces during sheardisplacement as well. For our samples, the adhesion value is maximizedat approximately 75 μm of shear displacement before retraction. After 75μm of shear displacement, the fibers were observed to begin to contacteach other, resulting in premature detachment, which results in loweradhesion during retraction. Another reason for the decrease in adhesionfor experiments with higher shear displacements is that many of thefibers begin to detach from the indenter during the shear displacementdue to high extension. When the fibers detach during the sheardisplacement phase, they do not contribute to the adhesion during theretraction phase, and the resulting adhesion is low. The significantdifference in the adhesion in the ‘gripping’ and ‘releasing’ directionssuggests that, like the gecko's footpads, the angled tip microfiberadhesives can provide controlled levels of adhesion to a surface vialoading in the ‘gripping’ direction, and can be easily separated from asurface via shear motion in the ‘releasing’ direction.

FIG. 12( c-e) shows profile views of angled mushroom tip fibers at theinstant before final detachment after varying shear displacements. Anyshear displacement in the ‘releasing’direction resulted in negligiblefiber extension and very low adhesion as the fibers slid out of contactwith the indenter (FIG. 12 c). In the ‘gripping’ direction, the fibersstretched further before detaching when displaced 75 μm in shear (FIG.12 e) compared to the detachment after a shear displacement of 50 μm(FIG. 12 d), which is expected from the results in FIG. 12 b. Theseimages demonstrate the significant difference in contact behavior fordisplacements in the ‘gripping’ and ‘releasing’ directions. The profileview also allowed direct observations of the fiber-fiber collisionswhich often resulted in immediate detachment. Although close fiberspacing can increase the number of fibers in contact with a surface fora given area, it limits the maximum size of the tips (the tips can mergeduring fabrication) and prevents long-range independent motion of thefibers. Increasing fiber spacing, altering the fiber angle orientation,or arranging the fibers in different patterns may increase the adhesiveperformance of the fibers by increasing the distance that fibers canextend before encountering a neighboring fiber.

As a demonstration of the macroscale adhesion of the directionalmicrofiber array, a small area (1 cm²) of a sample with 14° tip anglewas attached to a glass slide 70 which supported a hanging weight of 1kg in pure shear in the ‘gripping’ direction, an interfacial shearstrength of ˜100 kPa (FIG. 13 a), which is within the range of measuredinterfacial shear strength of gecko toes on smooth surfaces (88−200kPa). When reversed to the ‘releasing’ direction, the same sample wasable to support only 200 g (˜20 kPa) as illustrated in FIG. 13 b.However, for both of these experiments, the fiber sample could onlysustain the load for tens of seconds before detaching. The highestsustained loading over five minutes was 500 g (˜50 kPa) in the‘gripping’ direction. The sample was a directional polyurethanemicrofiber array with 14° angled tips adhering to smooth glass cansupport.

1.3.2 Summary

We have described embodiments of the present invention in which fiberarray constructs are created by dipping an angled fiber array into athin film of liquid polymer and then pressed against a substrate to formspecialized tips with controllable orientation to the fibers. Theseconstructs exhibit similar shear adhesive strength to the gecko lizard'sfeet on smooth surfaces, as demonstrated with macro-scale support ofsignificant loads (1 kg/cm²). These adhesives exhibit directionalcharacteristics, gripping when loaded in one direction, and releasingwhen loaded in the opposite shear direction. We have shown that theadhesion can be controlled by varying the shear displacement beforeloading in the normal direction. The angled tips of the fibers create alarger contact area and are responsible for the observed shearanisotropy. We have identified tip area as a main design parameter forthe magnitude of the interfacial shear strength, and the tip angle as adesign parameter to control the anisotropy ratio. The fabricationmethods described in this invention can be easily extended to smallersize scales and stiffer materials to more closely mimic the gecko'sadhesive structures. The high magnitude anisotropic adhesion of thesematerials may enable efficient gripping and releasing of structures.Additional embodiments of the invention will now be described.

1.4 Multi-Level Hierarchical Fibers

In other embodiments of the present invention, the fiber arraysfabricated according to the methods described above, are again placedinto a thin film or liquid polymer. In these embodiments, however,instead of then pressing the wet polymer at the tip of the fibers onto aflat surface, the wet polymer is pressed onto either an array of smallerscale fibers, or onto a mold to create an array of smaller scale fiberson the tips of the fiber array. These methods result in a hierarchicalfiber array construct, as described in further detail below. Thesestructures provide improved adhesive characteristics for adherence touneven and rough surfaces, and mimic the hierarchical fiber structuresobserved in nature.

The motivation for the creation of hierarchical structures is to providegreater adhesion to uneven and rough surfaces. Adaptation to uneven andrough surfaces is a major feature of biological fibrillar adhesives.Most natural and man-made surfaces are not perfectly smooth, andtraditional adhesives are typically less effective on rougher surfaces.Fibrillar adhesive materials with large areas and high uniformity can befabricated according to the methods of the present invention describedbelow. We also describe experimental results, which characterize theadhesive performance of the hierarchical materials against a smooth flatpunch and a smooth curved surface. The performance results are comparedto a flat control sample. Furthermore, we describe observations that 21were made about the interaction of fibrillar adhesives with unevensurfaces by viewing these interactions from the side with a microscope.

One advantage of fibrillar adhesives over flat unstructured adhesives isthat each fiber deforms independently, which allows them to accessdeeper recessions to make contact. Even with the reduced total area dueto the spaces between the fibers, the actual contact area can be greaterthan that of a flat adhesive in contact with a rough surface (FIG. 1).When a flat adhesive contacts a rough surface, contact is only made atthe highest asperities, and deformations of the bulk layer is relativelysmall. This leads to an overall low contact area. Because of theirstructures, fibrillar adhesives have a much lower effective Young'smodulus, and can deflect more to conform to surface roughness. Inaddition, the low effective modulus prevents the material fromattempting to return to its original shape from stored elastic energywhile attached to a surface, effectively peeling itself away from thesurface as seen in unstructured polymers. This allows larger surfaceroughness asperities to be tolerated as well as some forms ofcontamination. Although the contact area at each tip can be small, thesummation of the contact areas of all of the fibers in contact can bequite significant, particularly if the fibers can stretch or deflect andremain in contact for large extensions.

Another advantage of fibrillar surfaces is their ability to enhanceadhesion by contact splitting. If contact is split into many finerindependent contacts, adhesive strength increases due to load sharing.However, adhesive force is directly proportional to both adhesivestrength and total contact area. To exploit the advantage from fibrillaradhesives, the enhancement from contact splitting must compensate forthe reduction in contact area due to the lost area between the fibers.

1.4.1 Hierarchical Structures in Nature

In nature, the most advanced fibrillar dry adhesives are found in theheaviest animals such as the tokay gecko which can weigh up to 300grams. In comparison to the insects whose bodies are much lighter and donot require high performance adhesion, these animals have more complexadhesive pads with many levels of compliance including their toes, foottissue, lamellae, and fibers. Additionally, these fibers branch from amicron-scale diameter to sub-micron diameter tip fibers. The fiberstructure is similar to a branching tree or a broom. This multi-levelhierarchy allows the adhesives pads to conform to surface roughness withvarious frequency and wavelength scales. The toes and tissue conform tolarge-scale (mm scale) roughness, and each subsequent level conforms toroughness at its corresponding size-scale. Finally, the sub-micron tipfibers can access the smallest surface valleys.

FIG. 14 illustrates a hierarchical structure that allows roughnessadaptation to small and large wavelength and amplitude of surfaceroughness. In particular, a two level hierarchy is illustrated in FIG.14 where the large base fibers or stem 22 conform to the low-frequency,high amplitude roughness, while the tip fibers 60 conform to the highfrequency, low amplitude roughness. Furthermore, the smaller tip fibers60 have small endings, which are more likely to lie flat against theadhering surface due to their size scale. Where a large fiber tip mayencounter roughness underneath the tip, the surface may appear locallyflat at the length scale of the smaller fibers' 60 tips. The smallerfibers 60 may be formed of the same material as the large base fibers 22and may be, for example, another layer of stems, such as second layerstems. The smaller fibers 60 may be formed, for example, with a moldingprocess as described herein or by other processes. The smaller fibers 60may also be made from a different materials than the large base fibers22, such as with carbon nanofibers of other materials, as describedherein. Although this embodiment of the invention has been illustratedwith two layers or hierarchies of stems, the present invention alsoincludes dry adhesives with more than two layers of stems.

This type of multi-level structure is desirable for synthetic fibrillaradhesives as well. In this section, we disclose several fabricationtechniques for creating hierarchical synthetic fibers according to thepresent invention. These methods result in hierarchies from themillimeter scale to sub-micron scale. Fabrication results are alsodemonstrated and described. Finally, hemispherical indenter tests areused to examine the effect of hierarchy on adhesion and interfacetoughness.

1.4.2 Fabrication

The present invention includes several embodiments to fabricatefibrillar structures with multiple levels of hierarchy. These methodsspan the size scales from millimeter scale molding to nanoscale carbonnanofiber embedding. The following sections detail the fabricationprocesses and provide experimental 23 results of these techniques.

1.4.3 Nanoscale Hierarchy

In order to reach into the smallest recesses of a surface, the distalfibers of an adhesive pad should have sub-micron diameters, as seen inthe gecko's setae. It is possible to create synthetic fibrillar surfaceswith nanoscale diameter tip fibers by embedding vertical arrays ofcarbon nanotubes or carbon nanofibers into the tips of base fibers.

In one embodiment of the present invention, the mushroom tip fabricationprocess detailed previously is altered to enable the embedding ofsmaller scale fibers 60, such as carbon nanofibers or carbon nanotubes,into the tips 28 of polyurethane fibers.

FIG. 15 illustrates one embodiment of that process according to thepresent invention. In general, the process is for embedding carbonnanotubes or carbon nanofibers, or other structures 60 into the tips 28of base fibers to form a hierarchy. In FIG. 15 a, fibers or stems 22 aredipped into a liquid polyurethane layer 40. In FIG. 15 b, the ends ofthe fibers are coated with liquid polyurethane 40. In FIG. 15 c, thefiber array is placed into contact with a vertical array of nanofibersor nanotubes or other structures 80 which will form the second layerstem 60. In FIG. 15 d, the fiber array is peeled from the surface,retaining the embedded nanofibers 80 as a second layer stems 60. FIG. 15e, is an illustration of the stacked conical structure of CarbonNanofibers that may be used with the present invention. The widening ofthe conical structure near the base of the fibers 80 makes them mostlikely to fracture at this point.

The process illustrated in FIG. 15 will now be discussed in more detail.The process utilizes an array of smaller fibers 80, such as carbonnanofibers or carbon nanotubes or other structures on, for example, acarrier wafer or chip 82. In the process, a base fiber 22 array isdipped into liquid polyurethane 40 (FIG. 15 a) and picks up a layer ofthe liquid 40 on the tips of each fiber (FIG. 15 b). After waiting sometime to allow the liquid to partially cure, increasing its viscosity,the material is then placed onto the top of the vertical nanofiber 80array (FIG. 15 c). At this point, the liquid polyurethane 40 is pulledinto the nanofiber 80 array by capillary forces. These forces areextremely strong, due to the small spacing and large surface areabetween the fibers 80, so low viscosity liquid polyurethane 40 would becompletely absorbed. With proper viscosity, the liquid polyurethanelayer is partially absorbed, resulting in a branch-like structure (seeFIG. 16 b). After curing, the material construct is mechanically peeledfrom the carrier wafer 82, breaking off the nanofibers 80 at theirbases. The final structure is a hierarchical fiber with an extremelyrobust embedding of nanoscale diameter fibers 60 at the tips.

Vertical arrays of carbon nanofibers 60 were used in one embodiment ofthe present invention. Those skilled in the art will recognize thatother small scale or nanofiber arrays could be used. Carbon nanofibershave sufficient stiffness to prevent lateral collapse and are able to beclosely spaced. Although carbon nanofibers have high stiffness, theyalso can be grown to high aspect ratios, allowing them to be compliantin the vertical direction. Another advantage of carbon nanofibers forthis process is that the weakest part of the structure is at the basewhere the fiber meets the carrier wafer, due to a widening of thecone-shaped carbon sheet structure near the interface (FIG. 15 e). Thisweakness ensures that the fibers will break at this point whenmechanically peeled, resulting in a uniform height for all of thefibers.

Initial results (FIG. 16) confirm that embedding nanofibers at the tipsof polyurethane base fibers using the above process is feasible. FIG. 16a illustrates a Scanning Electron Micrograph of carbon nanofibersembedded into the tips of polyurethane base fibers to form ahierarchical fiber structure. FIG. 16 b illustrates a detailed view ofthe branching structure and uniform height of the carbon nanofibers.

In another embodiment of the present invention, methods are provided tofabricate hierarchical structures with specialized tips on the smallerscale fibers. As we have shown previously as well as observed in naturalfibrillar adhesives, widened tips provide a significant increase inadhesion. We have developed a tip fabrication process that allows thetip fiber shape to be controlled by micro-molding.

In this process, after the previously detailed dipping of base fibers 22in a liquid polymer layer 40, the fibers 22 are placed onto an etchedsilicon wafer. This wafer has micron-scale diameter cylindrical holeswith a widened tip formed by Deep Reactive Ion Etching. Thesesilicon-on-oxide negative templates can be fabricated according to themethods described in U.S. patent application Ser. No. 12/448,243, whichis incorporated herein by reference.

FIG. 17 illustrates one embodiment of the process for fabricatinghierarchical fibrillar adhesives with controlled tip fiber shape. FIG.17 a illustrates base fibers 22 with mushroom tips 28 that are dippedinto a liquid polyurethane layer 40. The liquid polyurethane 40 may be,for example, on a carrier surface. FIG. 17 b illustrates that some ofthe liquid polymer 40 is retained by the tips 28. FIG. 17 c illustratesthe fiber 22/28 array placed onto an etched silicon mold 50, where theliquid 40 from the tips 28 is drawn into the negative features 52. FIG.17 d illustrates that after the polyurethane 40 has cured, the siliconmold 50 is etched away with, for example, a dry etching process. Thepolymer tips 40 may be removed mechanically by peeling from the mold 50,which is preferred when the mold 50 is made from a compliant materialsuch as silicone rubber.

One embodiment of the process illustrated in FIG. 17 will now bedescribed in more detail. The process begins with an array of basefibers 22 with flat tips 28, which are dipped (FIG. 17 a) into a thinliquid polyurethane layer 40 and then placed onto the negative siliconmaster template 50 (FIG. 17 c). Capillary forces draw the liquid polymerinto the cavities 52, which become filled beneath the base fibers 22/28.The material is then cured according to methods known to those skilledin the art, and the cured material becomes second layer stems 60 formedin the mold 50. The mold 50 is removed using, for example, Xe_(F2) dryetching to expose the second layer stems 60. Since the etching processoccurs over several hours, the base fibers 22/28 must be protected fromthe etching gases, as they are damaged by the prolonged exposure. Toprevent this, in one embodiment, the material construct is encapsulatedin protective polymer layer (not shown), such as polyurethane, whichseals the edges and does not allow the etching gases to reach the basefibers 22/28. When etching is complete, the final hierarchicalstructures remain (FIG. 17 d).

Material constructs fabricated with this process can be seen in FIG. 18.In particular, FIG. 18 illustrates Scanning Electron Micrograph ofpolyurethane hierarchical fibers with mushroom tips. The base fibershave approximately 50 μm diameter and the tip fibers have 3 μm diameterstems with 5 μm diameter tips.

One advantage of this fabrication method is that there is no constrainton the scale of the tip fibers or second layer stems 60. For example,nanoscale tip fibers 60 may be integrated into microscale base fibers 22and tips 28 with this technique.

An overview of the methods of making dry adhesives according to oneembodiment of the present invention will now be provided starting withFIG. 19.

FIG. 19 illustrates one embodiment of a method of forming a dry adhesive10 with a structure including a backing layer 20 and a stem 22, whereinthe stem 22 includes first 24 and second 26 ends on opposite sides ofthe stem 22, and wherein the first end 24 of the stem 22 is connected tothe backing layer 20. The second end 26 of the stem 22 is connected tothe tip 28. An example of such as structure is shown in FIG. 17.

Step 300 includes applying a liquid polymer to the second end 26 of thestem 22.

Step 302 includes molding the liquid polymer 40 on the stem 22 in a mold50, wherein the mold 50 includes a recess 52 having a cross-sectionalarea that is less than a cross-sectional area of the second end 26 ofthe stem 22.

Step 304 includes curing the liquid polymer 40 in the mold 50 to form atip 28 at the second end 26 of the stem 22, wherein the tip 28 includesa second layer stem 60, corresponding to the recess 52 in the mold 50;and

Step 306 includes removing the tip 28 from the mold 50 after the liquidpolymer 40 cures.

Many variations and modifications are possible with the presentinvention. Some of those variations and modifications. For example, thestem 22 may be perpendicular to the backing layer 20, or the stem 22 maybe non-perpendicular to the backing layer 20. Other examples areprovided below.

Step 306, removing the tip from the mold, can include etching the moldfrom the tip. For example, the tip 28 can be removed from the mold 50 byetching the mold 50 as opposed to, for example, pulling the tip 28 outof the mold 50. Other variations are also possible. If the mold 50 isetching from the tip 28, the method may also include covering the stem22 with a protective polymer layer, such as polyurethane, before etchingthe mold 50. This may be done, for example, to protect the stem 22 fromthe etching processes.

The method of the present invention can be used to make many variationsof dry adhesives. In one embodiment, the stem 22 is microscale and thesecond layer stem 60 is nanoscale. Other variations are also possible.For example, the present invention also includes microscale second layerstems 60 on milliscale stems 22, smaller microscale stems 60 on largermicroscale stems 22, and other variations. The present invention canalso be used to make dry adhesives with more than two levels of stems22, 60. For example, the present invention may be used to make dryadhesives with three levels of stems, four levels of stems, or more.

Step 308, molding the liquid polymer on the stem, may include fillingthe recess 52 in the mold 50 with the liquid polymer 40 via capillaryforces.

Step 300, applying a liquid polymer 40 to the second end 26 of the stem22, includes dipping the second end 26 of the stem 22 in the liquidpolymer 40 and removing the second end 26 of the stem 22 from the liquidpolymer 40 after the liquid polymer 40 is applied to the second end 26of the stem 22.

The present invention may also include bending the stem 22 relative tothe backing layer 20 while molding 302 the liquid polymer 40 on the stem22 in the mold 50. The present invention may also include bending thestem 22 relative to the backing layer 20 while curing the liquid polymer40 in the mold 40. If the stem 22 is bent while the liquid polymer 40cures, the tip 28 can be made to take on different shapes, depending onthe extent to which the stem 22 is bent, as described herein. Thebending of the stem may include applying a load to the backing layer 20.Furthermore, the stem may be bent in a direction away from aperpendicular orientation with the backing layer, as described herein.

FIG. 20 illustrates another embodiment of the present invention in whichfurther steps are performed after those described with reference to FIG.19.

Step 310 includes applying a liquid polymer to the second layer stem.

Step 312 includes molding the liquid polymer on the second layer stemwith a second mold, wherein the second mold includes a recess having across-sectional area that is less than a cross-sectional area of thesecond layer stem.

Step 314 includes curing the liquid polymer in the mold to form a tip onthe second layer stem, wherein the tip on the second layer stem includesa third layer stem, and wherein the third layer stem corresponds to therecess in the second mold.

Step 316 includes removing the tip on the second layer stem from thesecond mold.

FIG. 21 illustrates another embodiment of the present invention. Thisembodiment of the method will be described with reference to FIG. 19,although it may also be performed after the steps of FIG. 20.

Step 320 includes applying a liquid polymer 40 to the second layer stem60.

Step 322 includes inserting a plurality of fibers 80 into the liquidpolymer 40 on the second layer stem 60, wherein the plurality of fibers80 have a cross-sectional area which is less than a cross-sectional areaof the second layer stem 60.

Step 324 includes curing the liquid polymer 40 on the second layer stem60 with the plurality of fibers 80 in the liquid polymer 40.

Many variations and modifications are possible with this embodiment ofthe present invention. For example, the fibers may be nanotubes,nanowires, nanofibers, or other materials.

FIG. 22 illustrates another embodiment of the present inventionincluding a method of forming a dry adhesive 10 with a structureincluding a backing layer 20 and a stem 22, wherein the stem 22 includesfirst 24 and second 26 ends on opposite sides of the stem 22, andwherein the first end 24 of the stem 22 is connected to the backinglayer 20 and the second end 26 of the stem 22 is connect to the tip 28.

Step 330 includes applying a liquid polymer 40 to the second end 26 ofthe stem 22.

Step 332 includes inserting a plurality of fibers 80 into the liquidpolymer 40 on the second end of the stem, wherein the plurality offibers have a cross-sectional area which is less than a cross-sectionalarea of the second end of the stem.

Step 334 includes curing the liquid polymer with the plurality of fibersin the liquid polymer.

Many variations and modifications are possible with this embodiment ofthe present invention. For example, the fibers may be nanotube,nanofiber, nanowire arrays, or other structures. Also, the stem 22 maybe perpendicular or non-perpendicular to the backing layer 20.

Step 332, inserting a plurality of fibers into the liquid polymer 40,may include inserting a plurality of fibers connected to a base. Also,after step 334, curing the liquid polymer 40, the present invention mayinclude separating the plurality of fibers from the base.

1.4.4 Macroscale Hierarchy

The previously described techniques are intended to add tip fibers ontomolded base fibers to create a multi-layer fibrillar adhesive. Anothermethod to create a fibrillar structure is to create compliance in thebacking layer at a larger scale than the base fibers. Even simple slitsin an otherwise unstructured material has been demonstrated to increasethe average fracture energy of flat elastomers by an order of magnitude,due to inhibited crack propagation. This is seen in the feet of geckos,where the base fibers are attached to thin plate-like structures withspaces in between called lamellae. These lamellae increase macro-scalecompliance and prevent crack propagation. For synthetic adhesives,backing layer patterning can be integrated with one of the tip fibermethods described above to create a two-level hierarchy. Like thebiological lamellae, these fibers act to arrest cracks and increasecompliance.

Fabrication of macro-micro scale hierarchical structures is accomplishedusing a technique similar to that described above in FIG. 17. FIG. 23illustrates one embodiment of a fabrication process for macro-microhierarchical structures

Fabrication of the base fibers 22 is accomplished by using a rapidprototyping system (Invision HR, 3D Systems) to print plastic mastertemplates of the desired structures. It is possible to create fiberswith diameters as small as 250 μm with this hardware, but the techniqueis not limited to any particular size scale. Non-cylindrical geometriesare possible using this technique as well. The master template is moldedwith silicone rubber (HS II, Dow Corning) to create a negative mold.After separation from the master template, the negative mold is used toreplicate the base structures from polymers such as polyurethane. Wideflat mushroom tips 28 are added to these base fibers 22 in the same wayas described for micro-scale fibers. Instead of using the etched siliconmold as in the previous Section, a soft silicone elastomer mold 50 isused to create the tip fibers 60 (FIG. 230, and a subsequent dippingstep (FIG. 23 g-j) to add mushroom tips to these fibers 60. The finaltwo-level structure is illustrated in FIG. 23 k.

FIG. 24 illustrates a Scanning Electron Micrograph of a two levelpolyurethane fiber structure, with 50 μm diameter mushroom tipped fibersatop curved 400 μm diameter base fibers with 1 mm diameter mushroomtips.

FIG. 24 illustrates a typical two-level polyurethane fiber structurethat can be fabricated using this method. This sample is comprised of 50μm diameter fibers with 100 μm diameter mushroom tips atop 400 μmdiameter base fibers with 1 mm diameter mushroom tips. The curved basefibers demonstrate the feasibility of creating complex shapes. Theroughness of the base fibers is due to the relatively low resolution ofthe rapid prototype master template.

The larger length-scale of these dual-level hierarchical fibers, theroughness adaptation to larger amplitude rough surfaces should besignificantly increased. This effect will be investigated in detail inSection 1.4.6.

1.4.5 Three-Level Hierarchy

In another embodiment of the present invention, the macroscale hierarchyfabrication technique are combined with the microscale hierarchytechnique to fabricate three-level hierarchical fibers, each levelhaving mushroom shaped tips for increased area. Combining the processesis relatively straightforward, but does require several steps tocomplete. (FIG. 25). FIG. 25 illustrated one embodiment of the processflow for fabricating three-level hierarchical fibers according to thepresent invention. In this embodiment, smaller third level fibers areadded by the same method taught in the two-level description above. Theillustrated embodiment has first 22, second 60, and third 90 levels.

Many variations are possible. For example, it is possible to simplifythis process by doing several of the steps (FIG. 25 a-j) and then usingthe resulting structure as a master template. Forming a negativecompliant silicone rubber mold at this step allows fabrication of steps(FIG. 25 k-m) following a single molding step, rather than the manysteps it would require otherwise. In this way, the first steps must onlybe completed once to form the master 2-level structures.

Initial results of three-level hierarchical fiber fabrication arepromising. FIG. 26 illustrates Scanning Electron Micrographs of 3-levelhierarchical polyurethane fibers. FIG. 26 a illustrates curved basefibers with 400 μm diameter. FIG. 26 b illustrates base fiber tip withmid level 50 μm diameter fibers. FIG. 26 c illustrates mid-level fibersin detail. FIG. 26 d illustrates terminal third level fibers at the tipof the mid level fibers are 3 μm in diameter, 20 μm tall, and have 5 μmdiameter mushroom tips.

Polyurethane structures (FIG. 26) exhibit good uniformity with theexception of the terminal tip fibers. Some of the microscale tip fibersare collapsed due to their small diameters and high aspect ratios, inaddition to the large stresses from the final release step infabrication. Smaller scale fibers benefit from stiffer materials, so itis likely beneficial to use different materials for each of thehierarchical levels. This is easily accomplished using the samefabrication process, simply by dipping with alternate compatiblematerials for each level of hierarchy.

1.4.6 Experiments

Four samples were fabricated from polyurethane (ST-1060; BJBEnterprises), an unstructured control sample, a single level fibersample, a double level vertical sample, and a double level angledsample. The double level samples were fabricated using the techniquesdescribed in Section 1.4.4. The details of the samples can be seen inTable 1.

TABLE 1 Sample specifications. Total Base Base Base Contact Fiber FiberFiber Area Sample Type Material Height Diameter Angle FractionUnstructured ST-1060 NA NA NA 1005 Single Level ST-1060 NA NA NA   36%Double Level Angled ST-1060 1.75 mm 425 μm 20°   10% Double LevelVertical ST-1060  1.2 mm 300 μm  0° 19.5%

All of the samples, other than the unstructured sample, have identicalterminal fibers, with 50 μm diameter stems, 100 μm height, and 110 μmdiameter mushroom tips with 160 μm center-to-center spacing. Theunstructured sample was molded against the same substrate so that it hasthe same surface properties as the fiber samples. Since the terminalfibers are identical between the three fiber samples, the onlydifference between them is the contact area fraction, and the structurebeneath the terminal fibers. In the Single Level case, this structure isa solid backing layer of the polyurethane. In the hierarchical samples,this structure is an array of larger base fibers. The base fibers areintended to make the sample effectively more compliant. However, alongwith the increased compliance, the contact area fraction (area−openspace between fibers) is significantly reduced. The total contact areafraction for the Double Level samples is the product of the contact areafraction of the terminal layer (36%) and the contact area fraction ofthe base layer. The contact area fraction of the unstructured sample is100%.

FIG. 27 illustrates Scanning Electron Micrographs of Double Levelhierarchical fiber samples. FIG. 27 a illustrates Double Level Vertical,and FIG. 27 b illustrates Double Level Angled. The large areas betweenthe fiber tips significantly reduce the total contact area fraction.

The four samples were tested using a 12 mm hemispherical smooth glassindenter. Because the extension length of the Double Level samples ishigh (mm scale), a retraction speed of 200 μm/s was chosen to minimizethe duration of the experiments. Similarly, the approach speed was setto 50 μm/s. Although viscoelastic effects are present due to therelatively high strain rate, these experiments are intended to comparethe hierarchical structures to the previously characterized Single LevelFibers and unstructured samples in a relative manner, not to determinetheir quantitative adhesive characteristics. Five experiments wereperformed on the same area of each sample at each specified preloadbetween 2 mN and 400 mN.

The resulting performance curves are plotted together in FIG. 28. Inparticular, FIG. 28 illustrates the performance curves for unstructured,single level, double level angled, and double level vertical samplesagainst a 12 mm diameter glass hemisphere. Error bars represent standarddeviations. The double level vertical fibers generally exhibit thehighest adhesion.

Results from the experiments in FIG. 28 indicate that for low preloads,the four samples exhibit similar adhesion. However, for larger preloads,the adhesion of the two vertical fiber samples (Single Level and DoubleLevel Vertical) increase at a faster rate than the increase for theunstructured sample. The reason for this increase is that as theindenter is pressed further into contact with the fibers with increasingpreloads, the fibers deform and allow neighboring fibers to come intocontact with the indenter. This is true for all of the fiber samples,especially the Double Level samples, which have highly increasedcompliance. The contact zone of the indenter on the unstructured sampledoes not increase as much as in the case of the fiber samples, so theincrease in adhesion with increasing preloads is modest. The decrease inadhesion for the Double Level Angled sample for preloads greater than128 mN is results from detachment during the preloading phase when theindentation depth becomes too high. The angled fibers detach under highpreloads and do not contribute to the adhesion during separation.

Since a hemispherical indenter represents a special case of a roughsurface, these result suggest that the Double Level Vertical fibersprovide higher adhesion against surfaces with high amplitude (mm scale)roughness.

To examine the sample-indenter interaction in more detail, theForce-Distance data for the four samples are plotted together in FIG.29. In particular, FIG. 29 a illustrates Force-Distance curves for thesamples tested at a preload of 128 mN. FIG. 29 b illustrates Maximumadhesion. FIG. 29 c illustrates Adhesion pressures. FIG. 29 dillustrates Dissipated energy. FIG. 29 e illustrates Total Work ofAdhesion. The experimental parameters for these tests were the same asabove, and the preload was set to 128 mN. The unstructured sample saw ahigher preload due to over-shoot during the indenting phase, its highstiffness and the small time delay in stopping and retracting theindenter caused a higher preload than for the other more compliantsamples. The indentation depth (maximum positive distance) of theindenter for the unstructured sample and single level sample are similar(73 μm and 93 μm, respectively), with the fiber sample being morecompliant. The Double Level Vertical sample is significantly morecompliant, with an indentation depth of 305 μm, and the most compliantsample was the Double Level Angled sample with an indentation depth of350 μm.

Using the indentation depths of from these data, it is possible toestimate the size of the contact zone using the geometrical equationsfor a spherical cap. The contact zone area a_(cz) is found asa _(cz)=πΔ_(p)(2R−Δ _(p))  (2)

where Δ_(p) is the indentation depth and R is the radius of thehemi-spherical indenter. The contact zone areas for these tests werefound to be 2.7 mm², 3.5 mm², 12.8 mm², and 11.2 mm² for theUnstructured, Single Level Fiber, Double Level Angled, and Double LevelVertical samples, respectively. Multiplying the estimated contact zoneareas by the contact area fraction for each sample results in anestimate for the real contact area. For the four samples, the realcontact areas were found to be 2.7 mm², 1.26 mm², 1.28 mm², and 2.18 mm²for the Unstructured, Single Level Fiber, Double Level Angled, andDouble Level Vertical samples, respectively. Therefore, the enhancementsdue to contact splitting and load sharing for the Double Level Verticalsample increased the adhesion.

The adhesions, maximum negative force, for the samples are compared inFIG. 29 b. The Double Level Vertical exhibited the highest adhesion,followed by the Single Level Fiber, Double Level Angled, andUnstructured samples, respectively. The adhesion pressures, which arecalculated by dividing the adhesion values by the estimated contact zoneareas are shown in FIG. 29 c. The adhesion pressures of the hierarchicalsamples are significantly lower than the unstructured and single levelfiber samples, likely due to their significantly lower contact areafraction. Furthermore, the small contact area of the Unstructured andSingle Level Fiber samples means that the contact area of the indenterwas relatively locally flat (less than 100 μm of height change), whilethe contact area of the Double Level samples contacted parts of theindenter with over 300 μm of height difference. Despite the loweradhesion pressure of the Double Level Vertical sample, due to itsroughness adaptation characteristics, it was able to adhere to theindenter with higher adhesion than the other samples. The hierarchicalstructure was able to more than make up for a contact area fraction ofless than 20%, exhibiting the best adhesion performance against theuneven geometry of the indenter.

The Force-Distance data can be used to calculate the energy dissipatedduring detachment for each of the samples, which indicates the toughnessof an interface. This energy is seen in FIG. 29 as the area under theretraction curve for each sample. The high retraction extension of theDouble Level samples requires a higher amount of energy to be expendedduring detachment. FIG. 29 d shows the dissipated energy of each sample.Very little energy is required to separate the Unstructured sample,while the Single Level Fiber, 31 Double Level Angled, and Double LevelVertical each require increasingly more energy, with the Double LevelVertical sample requiring 39.4 times as much energy than theunstructured sample. FIG. 29 e shows the work of adhesion of eachsample, a value calculated by dividing the dissipated energy by theestimated contact zone area. The hierarchy samples, even with muchlarger contact zones, exhibited higher work of adhesion than theunstructured sample, with the Double Level Vertical sample exhibitingthe highest work of adhesion, with 9.6 times as much as the unstructuredsample.

The advantage of hierarchical fibers does not only appear at largepreloads, it is also evident at low preloads as well. FIG. 30illustrates Force-Distance curves for the samples tested at a preload of5 mN. In particular, FIG. 30 depicts Force-Distance data for the DoubleLevel Vertical sample along with the Single Level Fibers and theunstructured sample tested at a preload of 5 mN. In this test,hierarchical structures extended over 1.2 mm and adhered with over 96 mNafter being preloaded with only 5.5 mN, dissipating 10 times as muchenergy during detachment as the unstructured sample, and 7.8 times asmuch energy as the Single Level Fiber sample.

To examine the behavior of a hierarchical sample interacting with anuneven surface, an experiment was run while recording a video of theside view of the sample. The test data (force vs. time) is illustratedin FIG. 31. Frames from associated still side-view video images areshown below the data in the same figure showing the approach (FIG. 31a), maximum preload condition (FIG. 31 b), maximum adhesion (FIG. 31 c),the last frame before final detachment (FIG. 31 d), and the fibersreturned to their original configuration (FIG. 31 e). The edge of thesphere is outlined for clarity. During retraction, both the terminal tipfibers and base fibers are observed to stretch as the sample maintainscontact with the indenter for large extensions (FIGS. 31 c and 31 d).

1.5 Repeatability

FIG. 32 illustrates data indicative of the repeatability of the presentinvention. In particular, the normalized adhesion is fairly constantwith increasing numbers of experiments, indicating that the adhesivesretain their performance over many attachment and detachment cycles.

Although the present invention has generally been described in terms ofspecific embodiments and implementations, the present invention isapplicable to other methods, apparatuses, systems, and technologies. Theexamples provided herein are illustrative and not limiting, and othervariations and modifications of the present invention are contemplated.Those and other variations and modifications of the present inventionare possible and contemplated, and it is intended that the foregoingspecification and the following claims cover such modifications andvariations.

1. A method of forming a dry adhesive with a structure including abacking layer and a stem, wherein the stem includes first and secondends on opposite sides of the stem, and wherein the first end of thestem is connected to the backing layer, comprising: applying a liquidpolymer to the second end of the stem; molding the liquid polymer on thestem in a mold, wherein the mold includes a recess having across-sectional area that is less than a cross-sectional area of thesecond end of the stem; curing the liquid polymer in the mold to form atip at the second end of the stem, wherein the tip includes a secondlayer stem; corresponding to the recess in the mold; and removing thetip from the mold after the liquid polymer cures.
 2. The method of claim1, wherein the stem is perpendicular to the backing layer.
 3. The methodof claim 1, wherein the stem is not perpendicular to the backing layer.4. The method of claim 1, further comprising: applying a liquid polymerto the second layer stem; molding the liquid polymer on the second layerstem with a second mold, wherein the second mold includes a recesshaving a cross-sectional area that is less than a cross-sectional areaof the second layer stem; curing the liquid polymer in the mold to forma tip on the second layer stem, wherein the tip on the second layer stemincludes a third layer stem, and wherein the third layer stemcorresponds to the recess in the second mold; and removing the tip onthe second layer stem from the second mold.
 5. The method of claim 1,wherein removing the tip from the mold includes etching the mold fromthe tip.
 6. The method of claim 5, further covering the stem with aprotective polymer layer before etching the mold.
 7. The method of claim1, wherein the stem is microscale and the second layer stem isnanoscale.
 8. The method of claim 1, wherein molding the liquid polymeron the stem includes filling the recess in the mold with the liquidpolymer via capillary forces.
 9. The method of claim 1, wherein applyinga liquid polymer to the second end of the stem includes: dipping thesecond end of the stem in a liquid polymer; and removing the second endof the stem from the liquid polymer after the liquid polymer is appliedto the second end of the stem.
 10. The method of claim 1, furthercomprising bending the stem relative to the backing layer while moldingthe liquid polymer on the stem in a mold.
 11. The method of claim 10,further comprising bending the stem relative to the backing layer whilecuring the liquid polymer in the mold.
 12. The method of claim 11,wherein bending the stem includes applying a load to the backing layer.13. The method of claim 11, wherein bending the stem includes bendingthe stem in a direction away from a perpendicular orientation with thebacking layer.
 14. The method of claim 1, further comprising: applying aliquid polymer to the second layer stem; inserting a plurality of fibersinto the liquid polymer on the second layer stem, wherein the pluralityof fibers have a cross-sectional area which is less than across-sectional area of the second layer stem; and curing the liquidpolymer on the second layer stem with the plurality of fibers in theliquid polymer.
 15. The method of claim 14, wherein the plurality offibers are nanotubes, nanowires, or nanofibers.
 16. The method of claim1, wherein: the backing layer includes a plurality of stems; applying aliquid polymer includes applying a liquid polymer to the second end ofeach of the plurality of stems; molding the liquid polymer includesmolding the liquid polymer on the plurality of stems, wherein the moldincludes a plurality of recesses corresponding to the plurality ofstems, and wherein each of the recesses have a cross-sectional area thatis less than a cross-sectional area of the second end of thecorresponding stem; curing the liquid polymer includes curing the liquidpolymer in the mold to form a plurality of tips at the second end of theplurality of stems, wherein the tips includes second layer stemscorresponding to the recesses in the mold; and removing the stems andthe tips from the mold after the liquid polymer cures.